There really are 2 tests to pass. The first is whether the ETF calls the dividend qualified. The second is whether you personally with those shares met the required holding period for those qualified dividends to remain qualified for you.
So in the buy and hold for 3 days, NO, the VTI qualified dividend would not be qualified to you. Your personal holding period is important. And that is true of mutual funds as well.
Your broker may send you a corrected 1099-DIV after a couple months into the new year if you ended up buying on the last day of the year with the amount of qualified dividends changed for you.
Maybe read IRS publication 550: http://www.irs.gov/pub/irs-pdf/p550.pdf
Holding period. You must have held the stock for more than 60 days during the 121-day pe- riod that begins 60 days before the ex-dividend date. The ex-dividend date is the first date fol- lowing the declaration of a dividend on which the buyer of a stock is not entitled to receive the next dividend payment. When counting the number of days you held the stock, include the day you disposed of the stock, but not the day you acquired it. See the examples, below.
In Pub 550, there is Example 3 which clearly shows that both tests must be met for a mutual fund. An ETF is a fund.